Experimental quantum secure direct communication with single

photons

Jianyong Hu1, Bo Yu

1, Mingyong Jing

1, Liantuan Xiao

1, Suotang Jia

1, Guoqing Qin

2,3,4 and Guilu

Long2,3,4

1State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser

Spectroscopy, Shanxi University, Taiyuan 030006, ShanXi province, China; 2State Key Laboratory

of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing

100084, China; 3Collaborative Innovation Center of Quantum Matter, Beijing 100084, China;

4Tsinghua National Laboratory for Information Science and Technology, Tsinghua University,

Beijing 100084, China.

Abstract: Quantum communication holds promise for absolutely security in secret message

transmission. Quantum secure direct communication is an important mode of the quantum

communication in which secret messages are securely communicated over a quantum channel

directly. It has become one of the hot research areas in the last decade, and offers both high security

and instantaneousness in communication. It is also a basic cryptographic primitive for constructing

other quantum communication tasks such as quantum authentication, quantum dialogue and so on.

Here we report the first experimental demonstration of quantum secure direct communication with

single photons. The experiment is based on the DL04 protocol, equipped with a simple frequency

coding. It has the advantage of being robust against channel noise and loss. The experiment

demonstrated explicitly the block data transmission technique, which is essential for quantum secure

direct communication. In the experiment, a block transmission of 80 single photons was

demonstrated over fiber, and it provides effectively 16 different values, which is equivalent to 4 bits

of direct transmission in one block. The experiment has firmly demonstrated the feasibility of

quantum secure direct communication in the presence of noise and loss.

Keywords: channel noise and loss, DL04 protocol, frequency coding, quantum secure direct

communication, single-photons modulation

INTRODUCTION

Secure communication is not only vital in military use and national security, but also important in

modern everyday life. Quantum communication provides a novel way of communication with

provable security. There are different modes of quantum communication, where each mode

completes a specific task. Quantum key distribution (QKD) is the earliest and widely studied mode,1

where two remote users distribute securely a random key. In quantum secret sharing,2 a secret key is

shared among two or more agents through quantum channels, and the key could only be constructed

if the entire agents collaborate. With quantum secure direct communication (QSDC),3 secret

messages can be communicated directly through a quantum channel without first establishing a key.

In quantum teleportation,4 an unknown quantum state can be sent to a distant agent without actually

sending the particle physically. In quantum dense coding,5 two bits of information can be transmitted

by just sending a particle with only a single bit. A fundamental difference between quantum and

classical communication is the capability to detect eavesdropping on-site. Classical communication

has no means to find eavesdropping during its operation. In contrast, quantum communication can

detect Eve on-site, because according to quantum principle, any eavesdropping will cause change in

the states and leads a sharp increase in the error rate. During a QKD process, sampling measurements

are made constantly to estimate the error rate. If the error rate is lower than a given threshold, then

the communication is concluded safe and the transmitted data are retained as raw key. If the error

rate is higher than the threshold, the communication is considered insecure and the transmitted data

are discarded. Because this information leakage before detection of Eve, it is essential that data

transmitted in QKD be random, otherwise information will be leaked. Experimental development of

QKD has been fast, and has reached a distance of a few hundred kilometers.6

In some QKD protocols, such as the BB84 or BBM92 protocols,1,7

the random key is distributed

indeterminately. In the determinate QKD protocols,8-12

one user, Alice can first generate a random

key, and then deterministically sends it to the other user, Bob. Though there is a difference in

distributing the key, their key distribution nature does not change. The data transmitted must be

random, otherwise the data transmitted before Eve’s detection will be divulged. After the key is

established, it is used to encrypt the message into ciphertext and then be transmitted through a

classical communication to the other party. With deterministic QKD, the secret message transmission

can be varied. Namely, Alice first chooses a random key and uses it to encrypt the secret message

into ciphertext. Then Alice transmits the ciphertext to Bob through a quantum channel using the

deterministic QKD. If they are certain that no eavesdropper exists, Alice sends the key through a

classical channel to Bob. This is often called deterministic QKD communication, which is essentially

a determinate QKD process plus a classical communication.13

In contrast to QKD, QSDC sends secret information directly through a quantum channel with

provable security without setting up a key first,3 which is a great improvement to the classical

communication mode.14

Like QKD, the security of QSDC also relies on quantum principles such as

the no-cloning theorem, the uncertainty principle, correlation of entangled particles and nonlocality

and so on. In addition, QSDC uses a block transmission technique, proposed in Ref. 3. In the block

transmission,3 the quantum information carriers such as EPR pairs or single photons are transmitted

in block of N particles. Then eavesdropping check is performed on the block so as to determine if

there exists eavesdropping. Block transmission not only detects eavesdropping, but also avoids the

leakage of information before detection of Eve,3 hence enabling the direct secure communication. Of

course, QSDC can also transmit random numbers and be used as QKD. After the first QSDC

protocol (the efficient-QSDC protocol3) was proposed; many other QSDC protocols have been

constructed. In 2003, Deng, Long and Liu proposed the two-step QSDC protocol15

where the criteria

for QSDC were explicitly stated. QSDC protocols with high-dimensional entanglement,16-18

with

multipartite entanglement,19-21

with hyperentanglement22

were developed. However, entanglement is

not necessary for quantum communication. The first QSDC protocol with single photons was

proposed in Ref. 23, the so-called DL04 protocol. Afterwards, many QSDC protocols based on

single photons were proposed.24-26

The secure direct nature of QSDC makes it an important

cryptographic primitive. Protocols of quantum signature,27

quantum dialogues,28,29

and quantum

direct secret sharing30,31

were all constructed using QSDC. QSDC has become one of the hot

research topics in quantum communication in the last decade.

The DL04 protocol is the first QSDC protocol based on single photon,23

which is easier to implement

than those with entanglement sources. It has been experimentally demonstrated in some special

cases, namely the N=1 case of the DL04 protocol, denoted as DL04N1, or LM05, which is a robust

four-state two-way deterministic QKD protocol.32,33,34

Based on DL04N1, Deng et al constructed a

circular quantum secret sharing protocol,35

which has been experimentally demonstrated by Jin et al

over 50 km in fibers.36

DL04N1 protocol has been proved to be unconditional security recently.37

When there is noise in the channel, an adversary Eve can gain a certain amount of information by

hiding her presence in the channel noise. In these cases, the information leakage should be eliminated

by using either quantum error correction38

or quantum privacy amplification.39

However, quantum

privacy amplification is complex to implement, and it also ruins the direct communication picture as

it involves the merger and order reshuffling of photons. An efficient way to implement QSDC in

noisy channel is to use quantum error correction.38,40

As a matter of fact, post-processing can be

performed by using quantum error correction without using privacy amplification and reconciliation

in QKD.41

In this work, instead of using a complicated quantum error correction scheme, we

introduce a simple frequency coding scheme into the DL04 protocol and propose new QSDC

protocol, which we call simple-coded DL04 (SICO-DL04) protocol. In SICO-DL04 protocol, the

information is encoded on the spectrum of a sequence of single photons rather than on the single

qubits in the original DL04 protocol. SICO-DL04 can work efficiently in the presence of channel

loss and noise. We have demonstrated the SICO-DL04 protocol experimentally.

MATERIALS AND METHODS

Here we describe the SICO-DL04 protocol briefly. Suppose that Bob wants to send secret

information to Alice. The protocol contains the following four steps:

1) Alice prepares a sequence of N2 single photons. Each photon of the sequence is randomly in one

of the four states |0, |1, |+, and |, where |0 and |1 are the eigenstates of the Pauli Z operator,

and | = (|0 |1)/2 are the eigenstates of the Pauli X operator. Then Alice sends the photon

sequence to Bob, Bob acknowledges this fact.

2) Because of channel noise and loss, Bob receives only N1 single photons (N1<N2). He selects CN1

number (C is a positive number less or equal to 1/2) of photons randomly from the N1 received

photons for eavesdropping check by measuring them randomly in the X-basis or the Z-basis. Bob

tells Alice the positions, the measuring-basis and the measuring results of these measured

photons. Alice compares her results with those of Bob and obtains an error rate. If the error rate is

higher than the threshold, they abort the communication. If the error rate is less than the threshold,

the Alice-Bob communication is considered as safe, and the communication continues to step 3.

3) The remaining (1C)N1 received photons are used for encoding the secret information. He also

selects C(1C)N1 single photons as check bits for the Bob-Alice transmission, and applies

randomly one of the two operations, I = |00|+|11|, and U = iy=|01||10|, which does

nothing or flip the state of the photon. The rest of the single photons will be processed by a simple

frequency coding scheme, which will be described later.

4) Bob sends the encoded photon sequence back to Alice who can deterministically decode the

qubits by measuring the photons in the same basis she prepared, without demand for a classical

channel. Alice gets the bit value of each single photon in the sequence and their arrival time.

Because of channel loss, Bob receives only N (N(1C)2N1) photons in each block after

subtracting the check photons. Alice and Bob will also publicly compare the results of the

checking bits to ensure if there exists eavesdropping in the Bob-Alice transmission. Next, Alice

calculates the spectrum and determines Bob’s encoded bits and reads out the secret information.

Now we describe the simple frequency coding scheme. In the DL04 protocol, the information is

directly encoded on the single photon state, where 0 is encoded with I and 1 with U =

iy=|01||10| respectively. The operation U flips the state without changing the measurement

basis, namely,

0 1 , 1 0 ,U U

, | | .U U (1)

However, in a noisy channel, such a direct coding is difficult due to noise and loss. Instead of using a

single operation to encode a bit value, simple frequency coding uses a series of periodic operations

on a photon sequence to encode information. Bob flips the state in a sequence of photons according

to a periodic function with period T=1/f, where f is the modulation frequency that encodes the

information. Once Alice obtains the modulation frequency after she measures a sequence of single

photons, she gets Bob's information fully. The modulation signal Bob applies to flip the photon

sequence, after excluding the checking bits, is

2 (2 1) ,flip,

Operation

no flip, (2 1) (2 2) ,

T i T

T i T

nT n T

n T n T (2)

where T is the modulation signal period. Different T encodes different bit values. T is an phase

offset for each modulating signal, and it is random so that Eve could not guess what the period T.

The measured value that Alice obtains is denoted as 0 if there is no state change, and 1 if there is

state flip. She also records the arrival time i, for i=1, 2, 3,…, N, where N is the number of optical

photons that Alice measured in each block after subtracting the check photons. An illustrating

example is given in Table 1, where the initial states, the final states, the measured value x(i) and

arrival time i are shown.

Table 1. Polarization modulation of single photons

Of course, not all the photons can arrive and be detected by Alice because of the loss of optical fibre

and imperfect detection efficiency of single photon detector. Then nothing will be recorded for the

lost photons. This simple frequency coding scheme is robust against error and loss. The coding

frequency can be accurately determined from the sequence (x(i), i) using the discrete time Fourier

transform,

2

( ) ( )

1

i

Nj f

f i

i

X x e . (3)

This spectrum will have a peak at the coding frequency f=1/T. From the spectrum, Alice can easily

determine the coding frequency, hence reads out the encoded information.

For a given quantum communication system, there exists a finite maximum number Nc of frequency

channels,

max min 1

c

b

f fN

f , (4)

where fmax and fmin are the maximum and minimum modulation frequencies respectively; fb is the

channel frequency spacing. If Bob uses only a single frequency to modulate one single photon

sequence, then each block can send Nc values. However, the capacity can be enlarged considerably if

Bob loads more than one frequency component onto the photon sequence simultaneously. Assuming

Bob loads r frequency components on one single photon sequence. The effective degrees of freedom

are the total number of different combinations of r frequencies,

max

!

!( )!

C

C

NN

r N r

, (5)

which means one single photon sequence can carry b=log2 Nmax bits of information. The transmission

rate can be expressed as

2 max

span span

1log

bI N

T T , (6)

where Tspan is the time span, i.e., the time length of photon sequence. In an example with a 500 MHz

modulation bandwidth, fb=1.5 kHz, Tspan =1ms and frequency components r=3, the transmission rate

can reach I=42.5 kbps. This coding scheme is similar to the ultra-wide-band communication in the

field of wireless communication.42

With more sophisticated coding algorithms, the system

performance could be further improved.

RESULTS AND DISCUSSION

The experimental setup is shown in Fig.1. The encoding process is controlled by a field

programmable gate array (FPGA) device. In order to guarantee the security of the secret information,

the eavesdropping detection process must be finished before the encoding procedure. During the

eavesdropping detection procedure of the block, an optical fibre (with length L2) is used as a delay

line to store the encoded photons. In practical application, single photons are approximated by

attenuated weak light pulses. The photon number of coherent light pulse obeys Poisson distribution.

Because of this, there is a white noise in the spectrum of the measured sequence. The bandwidth of

the modulation frequency used in our experiment is about 400 kHz.43

In our experiment, we take

Nc=16 frequency channels within the 400 kHz bandwidth and frequency spacing of 25 kHz. The

results of the spectral analysis of the sequence (x(i), i) using Eq. (3) are shown in Fig. 2. It shows

that there is a peak at each of the modulation frequency among the white noise background. All

together there are 16 such peaks. Though the noise and loss of the quantum channel broaden the peak

and reduce the height of peak, the central frequency remains the same, which determines the coding

frequency accurately. This enables Alice to read out the information encoded by Bob. The

identification of the modulation frequency is possible only when the signal-to-noise is higher than 1.

Figure 3 shows the relationship between the signal and background noise with different mean photon

numbers. It indicates that with a bigger relative photon number per pulse, the modulation signal is

much higher than the background noise. We also draw the background noise distribution in Figure 3.

It is shown that as the mean photon number per pulse increases, the background noise remains low.

In our frequency coding experiment, the system repetition frequency is 10 MHz. The number of

photons used for spectrum calculation in a block is N=80. The time span of the single photon block is

Tspan =1ms. We take r=1, hence only one frequency channel will respond to the received signal at any

given moment, which means Alice can get log216=4 bits of information by processing one block of

data in one time span. The communication rate in the experiment is 4 kbps.

Now we discuss the security of the SICO-DL04 protocol briefly. Here we give a brief analysis of

the security of SICO-DL04. These results will give a rough estimate and rigorous unconditional

security proof of the protocol will not be presented in this paper. As we have discussed before, no

one can acquire the frequency information unless the length of the sequence (x(i), i) they collected is

long enough for spectrum calculation. If the mean number of qubits per pulse Eve obtained, REve, is

small enough, Eve cannot distinguish the modulation frequency from background noise. So, she

would not get any useful information. For a given quantum communication system, once all the

parameters such as mean photon number, communication distance, etc. have been set, the amount of

information that the receiver (or an eavesdropper) can obtain is predictable. When the single-photon

source is an attenuated laser pulse with mean photon number per pulse, the probability to have n

photons in a single pulse follows the Poisson distribution pn. The probability that an optical pulse

could be detected at the receiving end is44

det det1

[1 (1 (1 )) ] (1 )n

nn

P p C C

, (7)

where =10(2L1+L2)/10

is the optical attenuation due to the loss of the fiber (the total fiber length is

2L1+L2); L1 and L2 are the communication distance and the optical delay line at Bob side

respectively. is the optical fiber loss coefficient (typical value is 0.2 dB/km); det is the quantum

efficiency of the single photon detector.45,46

Equation (7) is valid if det pn n << 1 for all n. With

multiphoton pulses, Eve performs a quantum nondemolition measurement on the pulses as soon as

they exit Alice's station. When n=2 Eve stores one photon and sends the other one to Bob by using a

lossless channel. After Bob's encoding operation, Eve captures the photon again. In order to gain

Bob's secret information, Eve must judge whether the polarizations of the two photons are parallel or

antiparallel. As described in Ref. 47, there exists an optimal measurement which gives Eve a

conclusive result with probability 1/4. Eve discards all the inconclusive results and retains the

conclusive ones. The mean amount of effective photons that Eve gets within an operation-cycle is

2L /102

Eve 2

1[10 (1 )]

4

nR p C , (8)

where p2 is the Poisson distribution component for n=2. When n=3, there exists a measurement M

that provides a conclusive result about whether the polarization is flipped or not with a probability

1/2 (ref. 48). For pulses with three or more photons, she executes M, if the outcome is not conclusive

she blocks these pulses, and if the outcome is conclusive she prepares a new photon in the same state

and forwards it to Bob. After Bob's encoding operation, Eve measures the photon again on the

backward trip to see whether the polarization state has been flipped. From these operations, the mean

amount of effective qubits that Eve can get is

2 /103

Eve3

1[10 (1 ) ]

2

Ln

nn

R C p . (9)

Both eavesdropping methods do not cause any bit error, which means Eve could not be detected

during such an eavesdropping process.

In a noisy channel, Eve may also gain a certain amount of data without being detected by hiding her

presence in the noise if she replaces the noisy channel by an ideal one and sends another photon

prepared by herself to Alice. She could acquire a fraction 4e of the qubits on the forward Alice-Bob

channel, where e is the bit error rate caused by channel noise. The factor 4 arises because there is a

50% chance for Eve to pick the correct basis, and for those she picks the wrong basis she has another

50% chance of not causing a bit error. The mean qubits that Eve can get is

1 2( ) /101

Eve 14[10 (1 )]L LnR p e C . (10)

Considering all the strategies, the mean number of photons that Eve eventually gets is

1 2 3

Eve Eve Eve Eve+n n nR R R R . (11)

The number of photons that Alice gets and the transmission rate of Alice respectively could be

derived from equation (6)

1 2

Alice det10 (1 )（2 + ）/10 L LR C , (12)

AliceAlice

span

bR

INT , (13)

where b is the bit-string length of the secret information encoded in a single photon sequence, and N

is the number of qubits that Alice received from a single photon sequence for information recovery

in one time span. The identification of the modulation frequency needs enough data for spectrum

calculation. Although Eve gets some qubits, it does not mean that she can get any information bit.

From the viewpoint of information theory,49

Eve cannot get the information bits more than b when

the number of qubits she gets is smaller than b. Therefore, considering the equations (12~13), the

condition of security is RAlice / REve > N / b. The secure information bits per pulse and secure

communication distance were shown in Figure 4. The distance depends on the intensity of laser

pulses. For weak laser pulses, the secure distance is about 10 kilometers, which is similar to two-way

QKD with weak laser pulses.

CONCLUSIONS

In summary, we presented a new practical QSDC protocol based on single photons, the SICO-DL04

protocol, in which a novel quantum frequency coding scheme was developed. In the protocol, instead

of encoding the bit values on the individual photons, the information is encoded in the modulation

frequencies which flip the states of photons in a sequence periodically. Because the information is

encoded on the statistical properties of the sequence, it is robust against channel loss and noise. The

SICO-DL04 protocol does not require privacy amplification procedure which ruins the quantum

secure direct communication picture. The frequency coding scheme can also adopt several

modulation frequencies simultaneously, increasing considerably the amount of information that a

block of single photons can carry. It is also simpler than protocols encoded with complicated

quantum error correction code. The security of the protocol is also carefully analyzed, taking into

major eavesdropping attack strategies and channel noise and loss.

We have demonstrated the SICO-DL04 protocol experimentally using existing technology. This is

the first time that the block transmission has been demonstrated, hence the first experimental

demonstration of QSDC. In our experiment, the transmission is carried out in blocks, each block

contains 80 photons. The range of the modulation frequency is 400 kHz, and frequency spacing is 25

kHz. Each single photon sequence can transmit one of the 16 frequency values, which is 4 bits of

information. A transmission rate of 4 kbps has been demonstrated in the experiment. The experiment

has firmly demonstrated the principle of QSDC with current technology and practical channel noise

and loss.

ACKNOWLEDGMENTS

The project is sponsored by 973 Program (2012CB921603), 863 Program (2011AA010801), the

Natural Science Foundation of China (11174187, 10934004 and 11204166), the Doctoral Foundation

of the Education Ministry of China (20121401120016) and PCSIRT (IRT 13076). Qin GQ and Long

GL are supported by National Natural Science Foundation of China under Grant Nos. 11175094 and

91221205, and the National Basic Research Program of China under Grant No. 2015CB921001.

______________________________________________________

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Figure 1 Schematic diagram of experimental setup of SICO-DL04 protocol. PBS: Polarization beam

splitter; Att: Variable attenuator; PC: Polarization controller; BS: Beam splitter; CM: Control model;

FPGA: Field Programmable Gate Array; SPD: Single photon detector. The distance between Alice

and Bob is L1, and the delay line length is L2.

Figure 2 The modulation spectrum. The y-axis is the Fourier transformed amplitude in Eq.(3).The

different colors represent different modulation frequencies, hence different values of information. If

each block of photons is modulated by a single frequency, then it carries 24=16 values, or 4 bits. The

background white noise is due to the imperfect single photon detector, channel noise.

Figure 3 The signal and background noise distribution of the modulation spectrum. The x-axis is the

average number of photon counts per pulse that Alice detects. The colored areas are the distribution

of the background noises, where the colors represent the relative probability of the noises with the

respective amplitudes. The red line represents the amplitude of the modulation peak. The modulation

frequency is chosen as 200 kHz. The system repetition frequency is 10 MHz.

Figure 4 The transmission bit per pulse versus the communication distance. The dotted line is the

cut-off line of the secure communication area. The solid lines with different color represent different

mean photon number per pulse (µ=0.19, 0.17, 0.15, 0.13, 0.11, 0.9, 0.7, 0.5, 0.3, 0.1, from top to

bottom). Here det=0.32, e=0.5%, =0.2 dB/km, L2=L1, C=1/2.